Generative AI, such as image generation models and large language models, stands to provide tremendous value to end-user programmers in creative and knowledge workflows. Current research methods struggle to engage end-users in a realistic conversation that balances the actually existing capabilities of generative AI with the open-ended nature of user workflows and the many opportunities for the application of this technology. In this work-in-progress paper, we introduce participatory prompting, a method for eliciting opportunities for generative AI in end-user workflows. The participatory prompting method combines a contextual inquiry and a researcher-mediated interaction with a generative model, which helps study participants interact with a generative model without having to develop prompting strategies of their own. We discuss the ongoing development of a study whose aim will be to identify end-user programming opportunities for generative AI in data analysis workflows.